There's actually a parity to the positions of the pieces that most people don't seem to know about. If you flip an edge or twist a corner, the whole cube becomes unsolvable.
You can also make it unsolvable by swapping stickers because each piece is unique. There is only one red/white/blue corner and only one green/yellow edge. Assuming standard color arrangement, there is no piece with both yellow and white, or both blue and green, or both red and orange.